A bookshelf is to hold $6$ literature books, $3$ geometry books and $7$ algebra books, arranged in random order. What is the probability that the books are arranged so that the first book on the shelf is a math book? Express your answer as a common fraction.
Each book is equally likely to be first on the shelf. There are $3+7=10$ math books out of $6+3+7 = 16$ books total, so the probability that the first book is a math book is $\boxed{\frac{5}{8}}$.